"Homeland" vs. "motherland" vs. "fatherland"

Solution 1:

The main semantic difference in English is that while all terms refer to one's native land or country of origin, motherland and fatherland also have the connotation of the land of one's ancestors.

Therefore, motherland/fatherland aren't as often applied to countries in the Americas, even if many of us have lived here for a dozen generations or more.

Solution 2:

The term homeland is relatively recent in U.S. English. It debuted in Webster's Eighth Collegiate Dictionary (1973) with the definition, "native land: fatherland." Subsequently, the Ninth Collegiate (1983) added a second definition: "a state or area set aside to be a state for a people of a particular national, cultural, or racial origin." And the Tenth Collegiate (1993), as if to clarify that homeland in the second sense does not apply to the reservation system administered by the Bureau of Indian Affairs in the United States, added the words "esp : BANTUSTAN" to the second definition.

In contrast, the terms motherland and fatherland have appeared in Webster's dictionaries since the American Dictionary of the English Language of 1847. That dictionary defined motherland as "The land of one's mother or parents," and fatherland as "The native land of one's fathers or ancestors."

The Homeland Security Act, which created the U.S. Department of Homeland Security, was enacted quite recently (in 2002). This may help to explain why none of the fairly recent U.S. dictionaries I consulted includes a definition of homeland along the lines of "a core territorial possession, as designated by a national government." However, that meaning seems to be at the heart of homeland as used in connection with U.S. national security; and I wouldn't be surprised to see it emerge as a definition in future dictionaries, considering that the two existing definitions fail to cover that sense of the term adequately.

Solution 3:

Motherland isn't common in English. Fatherland I would avoid unless you are talking about a specific era of German history.

Homeland is the nearest normal term for your "country of origin" but is a lot less common and doesn't have the added deep meaning that say, "motherland" would in Russia.
As a result of the US airport security I don't think "Homeland" is going to become a popular patriotic term.